use the law of cosines. find x to the nearest tenth.

Explanation:

Step1: Recall Law of Cosines formula

The Law of Cosines for finding an angle in a triangle with sides (a), (b), (c) is (\cos C=\frac{a^{2}+b^{2}-c^{2}}{2ab}). In (\triangle ABC), let (a = 10), (b=13), (c = 22), and we want to find (\angle B=x^{\circ}). So (\cos x=\frac{10^{2}+22^{2}-13^{2}}{2\times10\times22}).

Step2: Calculate the numerator

[ \begin{align*} 10^{2}+22^{2}-13^{2}&=100 + 484-169\ &=415 \end{align*} ]

Step3: Calculate the denominator

(2\times10\times22 = 440)

Step4: Find the value of (\cos x)

(\cos x=\frac{415}{440}\approx0.94318)

Step5: Find the value of (x)

(x=\cos^{-1}(0.94318)\approx19.5^{\circ})

Answer:

(19.5)